proof of Abel lemma (by expansion)
1 Abel lemma
where, . Sequences , , , are real or complex one.
We consider the expansion of the sum
on two different forms, namely:
On the short way.
On the long way.
where a simplification has been performed. Notice that . By equating (2), (3), the last two terms cancel, 11Without loss of generality, may be assumed finite. Indeed we don’t need , but the proof is a couple lines larger. It is left as an exercise. and then, (1) follows.
|Title||proof of Abel lemma (by expansion)|
|Date of creation||2013-03-22 17:28:14|
|Last modified on||2013-03-22 17:28:14|
|Last modified by||perucho (2192)|